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To solve for the total resistance (\(R_T\)) of the given combination circuit, we first need to simplify the parallel section of the circuit and then add it to the series resistance. Here's how we can solve it step-by-step:

### Step 1: Identify the Components
- \(R_1 = 8 \, \Omega\)
- \(R_2 = 20 \, \Omega\)
- \(R_3 = 30 \, \Omega\)

### Step 2: Simplify the Parallel Section
\(R_2\) and \(R_3\) are in parallel. The formula for two resistors in parallel is:

\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{R_2} + \frac{1}{R_3}
\]

\[
\frac{1}{R_{\text{parallel}}} = \frac{1}{20} + \frac{1}{30}
\]

Let's calculate \(R_{\text{parallel}}\):

\[
\frac{1}{R_{\text{parallel}}} = \frac{3 + 2}{60} = \frac{5}{60}
\]

\[
R_{\text{parallel}} = \frac{60}{5} = 12 \, \Omega
\]

### Step 3: Calculate the Total Resistance
Now, \(R_1\) (8 Ω) is in series with the equivalent resistance \(R_{\text{parallel}}\) (12 Ω). The total resistance for resistors in series is:

\[
R_T = R_1 + R_{\text{parallel}}
\]

\[
R_T = 8 + 12 = 20 \, \Omega
\]

### Step 4: Answer
The total resistance \(R_T\) of the circuit is **20 Ω**.

Would you like more details, or do you have any questions?

### Related Questions:
1. How do you calculate the total resistance for more complex circuits involving multiple parallel and series combinations?
2. What is the difference between resistors in series and parallel in terms of voltage and current distribution?
3. How would adding another resistor in series or parallel affect the total resistance of the circuit?
4. Can the power dissipation in each resistor be calculated from the given total voltage? How?
5. How does Ohm's Law apply to combination circuits, and how can it be used to solve for current or voltage in specific components?

**Tip:** Always start by simplifying the most complex parts of a circuit (like parallel sections) before adding series resistances.

Calculate the total resistance for this combination circuit. Remember to simplify the parallel section first.

Learn how to calculate the total resistance of a combination circuit, with resistors in series and parallel. This step-by-step guide walks through simplifying parallel resistors and adding series resistors to find the total resistance.

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